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A137538
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Number of permutations in S_n avoiding 25{bar 1}34 (i.e., every occurrence of 2534 is contained in an occurrence of a 25134).
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1
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1, 1, 2, 6, 23, 104, 532, 3004, 18426, 121393, 851810, 6325151, 49448313, 405298482, 3470885747, 30965656442, 287083987270, 2759838731485, 27458514900626, 282264050120512, 2993392570828096, 32704759586810036, 367673428857985261
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OFFSET
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0,3
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COMMENTS
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A permutation p avoids a pattern q if it has no subsequence that is order-isomorphic to q. For example, p avoids the pattern 132 if it has no subsequence abc with a < c < b.
Barred pattern avoidance considers permutations that avoid a pattern except in a special case. Given a barred pattern q, we may form two patterns, q1 = the sequence of unbarred letters of q and q2 = the sequence of all letters of q.
A permutation p avoids barred pattern q if every instance of q1 in p is embedded in a copy of q2 in p. In other words, p avoids q1, except in the special case that a copy of q1 is a subsequence of a copy of q2.
For example, if q = 5{bar 1}32{bar 4}, then q1 = 532 and q2 = 51324. p avoids q if every for decreasing subsequence acd of length 3 in p, one can find letters b and e so that the subsequence abcde of p has b < d < c < e < a. (End)
The number of permutations of length n avoiding the dashed pattern 1-42-3. - Andrew Baxter, May 17 2011
Apparently, also the number of permutations of length n avoiding the barred pattern 23{bar 1}54, which are the same as the permutations avoiding dashed pattern 1-24-3. - Andrew Baxter, May 17 2011
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KEYWORD
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nonn
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STATUS
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approved
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